x1 is a bijective function / isomorphism from x2 to x3, with inverse x4, in system / category x5; x1 has an inverse; x1 is a function that is injective and surjective; x2 and x3 are isomorphic; x1 is invertible.
x1=fan1=fr1 is a bijective function / isomorphism from x2=fan2 to x3=fan3, with inverse x4, in system / category x5; x1 has an inverse; x1 is a function that is injective and surjective; x2 and x3 are isomorphic; x1 is invertible.